Chief Inspector was a title for some police officers.
After Professor Peach was found murdered in December 1926, the Tenth Doctor used his psychic paper to establish himself as Chief Inspector Smith from Scotland Yard. (TV: The Unicorn and the Wasp)
Chief Inspector Patrick Mullen was an Irishman who worked for Special Branch in London during World War II. In November 1940, he helped the Seventh Doctor and Cody McBride investigate Cyberman activity, the Limehouse Lurker and George Limb. (PROSE: Illegal Alien)
In the 2000s, Chief Inspector Robert Lines worked for the West Ealing Police and was responsible for the missing case of Ashley Stafford. (PROSE: The Lost Boy, TV: The Lost Boy)